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Proof step 10 from proof exvalidrefs (previous step)

st[r -- _type] = typeval(mkclasstype(class0)), r ∈ st, mkfs(class, mkclasstype(class0), fieldvar) ' ∈ instfields(class0), class+∃(str, class0), goodfieldsandtypes(r, instfields(class0), st), r -- _type ∈ st, ∀ ty. type∃(str, ty) → (ty ≤ mkclasstype(class0) → ty = mkclasstype(class0)), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∀ ty. type∃(str, ty) → (ty ≤ st0[r -- _type] .type ↔ ty = st0[r -- _type] .type)) ∧ (∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ fs .type = st0[r -- _type] .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r = jvmref, cyclic(str, r, st), is_referencevalue(st[r -- mkfs(class, mkclasstype(class0), fieldvar) ']), is_abstract(class0), ∃ fs. fs ' ∈ instfields(class0) ∧ (is_reftype(fs .type) ∨ fs .type = abstract_type) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ is_referencevalue(st[r -- fs ']) ∨ ¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , goodfieldsandtypes(r, sks, st) ↔ (∀ sk. sk ∈ sks → goodfieldandtype(r, sk, st)) ,[st, sks, r] → [st, instfields(class0), r] ,F ,okfuns , ,gfts-all ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, instfields(class0), r)]]